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In a thin film of oil on water, if the thickness of the film is 0.1 mm and the w

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Question: In a thin film of oil on water, if the thickness of the film is 0.1 mm and the wavelength of light in air is 600 nm, what is the condition for constructive interference?

Options:

  1. 2t = (m + 0.5)λ
  2. 2t = mλ
  3. 2t = (m + 1)λ
  4. 2t = mλ/2

Correct Answer: 2t = mλ

Solution: 

For constructive interference in a thin film with a denser medium below, the condition is 2t = mλ.

In a thin film of oil on water, if the thickness of the film is 0.1 mm and the w

Practice Questions

Q1
In a thin film of oil on water, if the thickness of the film is 0.1 mm and the wavelength of light in air is 600 nm, what is the condition for constructive interference?
  1. 2t = (m + 0.5)λ
  2. 2t = mλ
  3. 2t = (m + 1)λ
  4. 2t = mλ/2

Questions & Step-by-Step Solutions

In a thin film of oil on water, if the thickness of the film is 0.1 mm and the wavelength of light in air is 600 nm, what is the condition for constructive interference?
  • Step 1: Understand that we are dealing with a thin film of oil on water.
  • Step 2: Identify the thickness of the oil film, which is given as 0.1 mm.
  • Step 3: Convert the thickness from mm to meters for easier calculations: 0.1 mm = 0.1 / 1000 = 0.0001 m.
  • Step 4: Note the wavelength of light in air, which is given as 600 nm.
  • Step 5: Convert the wavelength from nanometers to meters: 600 nm = 600 / 1,000,000,000 = 0.0000006 m.
  • Step 6: Recognize that for constructive interference in a thin film with a denser medium below (water), the condition is given by the formula 2t = mλ, where t is the thickness, λ is the wavelength, and m is an integer (0, 1, 2, ...).
  • Step 7: Substitute the values into the formula: 2 * 0.0001 m = m * 0.0000006 m.
  • Step 8: Rearrange the equation to find the values of m that satisfy the condition for constructive interference.
  • Thin Film Interference – The phenomenon where light waves reflected from the top and bottom surfaces of a thin film interfere with each other, leading to constructive or destructive interference based on the film's thickness and the wavelength of light.
  • Constructive Interference Condition – For constructive interference to occur in a thin film with a denser medium below, the path difference must be an integer multiple of the wavelength, represented by the equation 2t = mλ, where t is the film thickness, m is an integer, and λ is the wavelength of light in the medium.
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